Electrostatics of ions inside the nanopores and trans-membrane channels

A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical solution is used to calculate the electrostatic potential energy profiles for pores containing charged protein residues. Availability of a semi-exact interionic potential should greatly facilitate the study of ionic transport through nanopores and ion channels

Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors

In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of GSp(4,F), where F is a non-archimedean local field of characteristic zero with residue field of order q.Comment: 48 pages, 21 tables. Corrected an error in Table 16 for type V* representations (theta_11 and theta_12 were switched

Nocturia as an Unrecognized Symptom of Uncontrolled Hypertension in Black Men Aged 35 to 49 Years.

Background Hypertension is assumed to be asymptomatic. Yet, clinically significant nocturia (≥2 nightly voids) constitutes a putative symptom of uncontrolled hypertension. Black men with hypertension may be prone to nocturia because of blunted nocturnal blood pressure ( BP ) dipping, diuretic drug use for hypertension, and comorbidity that predisposes to nocturia. Here, we test the hypothesis that nocturia is a common and potentially reversible symptom of uncontrolled hypertension in black men. Methods and Results We determined the strength of association between nocturia (≥2 nightly voids) and high BP (≥135/85 mm Hg) by conducting in-person health interviews and measuring BP with an automated monitor in a large community-based sample of black men in their barbershops. Because nocturia is prevalent and steeply age-dependent after age 50 years, we studied men aged 35 to 49 years. Among 1673 black men (mean age, 43±4 years [ SD ]), those with hypertension were 56% more likely than men with normotension to have nocturia after adjustment for diabetes mellitus and sleep apnea (adjusted odds ratio, 1.56; 95% CI , 1.25-1.94 [ P<0.0001]). Nocturia prevalence varied by hypertension status, ranging from 24% in men with normotension to 49% in men whose hypertension was medically treated but uncontrolled. Men with untreated hypertension were 39% more likely than men with normotension to report nocturia ( P=0.02), whereas men whose hypertension was treated and controlled were no more likely than men with normotension to report nocturia ( P=0.69). Conclusions Uncontrolled hypertension was an independent determinant of clinically important nocturia in a large cross-sectional community-based study of non-Hispanic black men aged 35 to 49 years. Clinical Trial Registration URL : http://www.clinicaltrials.gov . Unqiue identifier: NCT 02321618

Effects of interatomic collisions on atom laser outcoupling

We present a computational approach to the outcoupling in a simple one-dimensional atom laser model, the objective being to circumvent mathematical difficulties arising from the breakdown of the Born and Markov approximations. The approach relies on the discretization of the continuum representing the reservoir of output modes, which allows the treatment of arbitrary forms of outcoupling as well as the incorporation of non-linear terms in the Hamiltonian, associated with interatomic collisions. By considering a single-mode trapped condensate, we study the influence of elastic collisions between trapped and free atoms on the quasi steady-state population of the trap, as well as the energy distribution and the coherence of the outcoupled atoms.Comment: 25 pages, 11 figures, to appear in J. Phys.

Quantum dynamical theory for squeezing the output of a Bose-Einstein condensate

A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the non-classical properties, such as sub-Poisson distribution and quadrature squeezing effect, mutually oscillate between the quantum states of the applied optical field and the resulting atom laser beam with time. In particular, it is shown that an initially squeezed optical field will lead to squeezing in the outcoupled atomic beam at later times.Comment: 6 pages, Latex file, Phys.Rev.A 63(2001)1560

Quasi-continuous atom laser in the presence of gravity

We analyse the extraction of a coherent atomic beam from a trapped Bose-Einstein condensate using a rf transition to a non-trapping state at T=0 K. Our quantum treatment fully takes gravity into account but neglects all interactions in the free falling beam. We obtain an analytical expression of the output rate and of the wave function of the extracted beam, i.e. the output mode of the ``atom laser''. Our model reproduces satisfactorily experimental data without any adjustable parameter.Comment: 4 pages, 2 figure

Program analysis is harder than verification: A computability perspective

We study from a computability perspective static program analysis, namely detecting sound program assertions, and verification, namely sound checking of program assertions. We first design a general computability model for domains of program assertions and correspond- ing program analysers and verifiers. Next, we formalize and prove an instantiation of Rice\u2019s theorem for static program analysis and verifica- tion. Then, within this general model, we provide and show a precise statement of the popular belief that program analysis is a harder prob- lem than program verification: we prove that for finite domains of pro- gram assertions, program analysis and verification are equivalent prob- lems, while for infinite domains, program analysis is strictly harder than verification

Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution

A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength become larger. The number of density matrices required is given by $3^{M}$ where $M$ is the number of timesteps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.Comment: 14 pages, 9 figure

Theory of output coupling for trapped fermionic atoms

We develop a dynamic theory of output coupling, for fermionic atoms initially confined in a magnetic trap. We consider an exactly soluble one-dimensional model, with a spatially localized delta-type coupling between the atoms in the trap and a continuum of free-particle external modes. Two important special cases are considered for the confinement potential: the infinite box and the harmonic oscillator. We establish that in both cases a bound state of the coupled system appears for any value of the coupling constant, implying that the trap population does not vanish in the infinite-time limit. For weak coupling, the energy spectrum of the outgoing beam exhibits peaks corresponding to the initially occupied energy levels in the trap; the height of these peaks increases with the energy. As the coupling gets stronger, the energy spectrum is displaced towards dressed energies of the fermions in the trap. The corresponding dressed states result from the coupling between the unperturbed fermionic states in the trap, mediated by the coupling between these states and the continuum. In the strong-coupling limit, there is a reinforcement of the lowest-energy dressed mode, which contributes to the energy spectrum of the outgoing beam more strongly than the other modes. This effect is especially pronounced for the one-dimensional box, which indicates that the efficiency of the mode-reinforcement mechanism depends on the steepness of the confinement potential. In this case, a quasi-monochromatic anti-bunched atomic beam is obtained. Results for a bosonic sample are also shown for comparison.Comment: 16 pages, 7 figures, added discussion on time-dependent spectral distribution and corresponding figur